A monument to Reagan's cuts in social welfare programmes: a homeless man in Washington, December 2008. Photograph: Jim Young/Reuters

Whatever Ronald Reagan had in mind for the shining city on the hill, it could not have been Washington. His lasting legacy to the capital city has been to make permanent an encampment of homeless people.

There always have been poor here, living in sharp contrast to the well-to-do political world of the city. But the homeless, during DC's recent history, appeared with Reagan's inauguration in 1981. They are testament to the first wave of conservative cuts in social welfare programmes, which, among other things, resulted in Reagan's famed "welfare queens'', along with the supposed malingerers who turned out to be mentally ill, being forced onto the street.

Administrations have come and gone but the homeless have become a permanent fixture in the city's life – a reminder that the conservative era launched by Reagan has little in common with Roosevelt's New Deal. There are now some 16,000 people who live on the streets of Washington in any one year, with at least 1,000 families among them. This city of 600,000, which considers itself progressive, young and hip, and where whites have now replaced blacks as a majority of the city's inhabitants, has sought to help homeless people with shelters, social programmes and housing. But there is not enough low-cost housing to make a serious dent.

Now, the new mayor, Vincent Gray, like officials elsewhere in the nation, has been faced with the hard choice of either increasing taxes or cutting the municipal budget. And as elsewhere, he has chosen to cut – and those cuts come down on the poor. Gray projects a need to pare $322m from the city's budget. That leaves a shortfall of $20.5m for homeless services in fiscal year 2012.

"Families with small children – even newborns – are being denied shelter,'' Eric Sheptock, himself homeless and one of that community's most articulate spokespeople, wrote in a recent email to his homeless supporters. He added: "A mother who gave birth on 10 February 2011 and left the hospital on the 12 February ended up sleeping in the Greyhound Station and in the stairwell of an unsecured apartment for the whole first month of the baby's life.''

But Gyant is one of the lucky ones. She eventually did find a job. In testifying last week before a city council committee, Gyant recalled how in her despair she tried to "make it like an adventure [for her children], so they didn't feel like Mommy was feeling.'' And then in a very soft voice in a room that had grown still, she said, "I plead with you to help families like mine in seasons other than hypothermia season."

Hypothermia season? What that means is that the city will turn the homeless into the streets and have them live there until the weather turns cold, and then, when they are facing temperatures at freezing point or below, the authorities will try to bring them into some sort of shelter. That's the beginning of "hypothermia season".' And all this just blocks from the FDR memorial with its sculptured replicas of the breadlines in the 1930s.

"This is the devastation of the homeless programmes of the District [of Columbia]," said Jim Graham, chairman of the council's human services committee after he heard Gyant's testimony, "Little babies in stairwells, bus stations and cars.''

As it stands presently, some 500 families are awaiting admittance to the DC's main family shelter at what used to be the district's general hospital. Already, DC has stopped processing admissions for new families – those not already in the system and waiting in line. Homeless families have increased in number in the district since 2007 by about 10%, according to Street Sense, a newspaper covering the homeless community, and written by a small staff along with homeless people.

Even this measure is not a foregone conclusion. The city council appears evenly divided on this modest increase, with representatives from prosperous areas in the north-west part of the city, including Georgetown, Cleveland Park and Capitol Hill, either arguing outright against a rise or dragging their feet. The opposing council members come from what are, historically, mostly white areas, where, as one black taxi cab driver bitterly pointed out to me, people are debating city funds for dog parks and bike lanes.

A recent poll by Hart Research Associates suggests most people living in the district, rich and poor, do not oppose a tax hike. So, as Ed Lazere, executive director of the DC Fiscal Policy Institute said, the problem here "does not appear to be the residents". Political insiders are guessing that opposition comes from business interests, especially those in real estate development, who can be important campaign contributors to elected city officials. Homeless advocates want to increase taxes along lines outlined by Lazere. That would raise the tax to 9.4% for those making $500,000 or more. As a practical matter, advocates concede there is scant chance of such a tax passing.

So, the stark symbols of Obama's Washington may turn out to be babies squalling in bus stops, and families living in cars.

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